A tank initially contains 100 gal of brine in which 20 lb of salt are dissolved. A brine containing 3 lb/gal of salt runs into the tank at the rate of 6 gal/min. The mixture is kept uniform by stirring and flows out of the tank at the rate of 5 gal/min. Let y represent the amount of salt at time t. Complete parts a through e.

Algebra & Trigonometry with Analytic Geometry
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ISBN:9781133382119
Author:Swokowski
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Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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A tank initially contains 100 gal of brine in which 20 lb of salt are dissolved. A brine containing 3 lb/gal of salt runs into the tank at the rate of 6 gal/min. The mixture is kept uniform by stirring and flows out of the tank at the rate of 5 gal/min. Let y represent the amount of salt at time t. Complete parts a through e.

A tank initially contains 100 gal of brine in which 20 Ib of salt are dissolved. A brine containing 3 Ib/gal of salt runs into the tank at the rate of 6 gal/min. The mixture is
kept uniform by stirring and flows out of the tank at the rate of 5 gal/min. Let y represent the amount of salt at time t. Complete parts a through e.
a. At what rate (pounds per minute) does salt enter the tank at time t?
Ib/min
b. What is the volume of brine in the tank at time t?
gal
c. At what rate (pounds per minute) does salt leave the tank at time t?
Ib/min
d. Write down and solve the initial value problem describing the mixing process.
dy
D, y(0) = 20.
dt
What is the solution to the initial value problem?
y =
e. Find the concentration of salt in the tank 19 min after the process starts.
Ib/gal
(Type an integer or decimal rounded to the nearest tenth as needed.)
Transcribed Image Text:A tank initially contains 100 gal of brine in which 20 Ib of salt are dissolved. A brine containing 3 Ib/gal of salt runs into the tank at the rate of 6 gal/min. The mixture is kept uniform by stirring and flows out of the tank at the rate of 5 gal/min. Let y represent the amount of salt at time t. Complete parts a through e. a. At what rate (pounds per minute) does salt enter the tank at time t? Ib/min b. What is the volume of brine in the tank at time t? gal c. At what rate (pounds per minute) does salt leave the tank at time t? Ib/min d. Write down and solve the initial value problem describing the mixing process. dy D, y(0) = 20. dt What is the solution to the initial value problem? y = e. Find the concentration of salt in the tank 19 min after the process starts. Ib/gal (Type an integer or decimal rounded to the nearest tenth as needed.)
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